Question

Which explains why the sequence 81, 3, 1/9 is arithmetic or geometric?

A) The sequence is arithmetic because it decreases by a factor of 3
B) The sequence is arithmetic because it decreases by a factor of 1/27
C) The sequence is geometric because it decreases by the factor 3
D) The sequence is geometric because it decreases by the factor 1/27

Answer 1

arithmetic -- next number is found by adding/subtracting
geometric -- next number is found by multiplying

to find the next term in a geometric, divide the second term by the first term
3/81 = 0.037 = 1/27
now see if you multiply by 1/27 will it equal the next term
3 * 1/27 = 1/9
3/27 = 1/9
1/9 = 1/9 (correct)

and you will see, that to get to the next number, you have to multiply by 1/27 and since you have to multiply to get the next term, it is a geometric sequence with a common ratio of 1/27

Answer 2

I think I get it. Thanks so much! :D

Answer 3

your so welcome :)